Abstract

A guaranteed deterministic problem setting of superreplication in discrete time is proposed as an alternative to the traditional probabilistic approach based on the use of the reference measure. Within the proposed framework, the reference measure is not needed, and aim of hedging of contingent claim is to guarantee coverage of possible payoff under the option contract for all admissible scenarios. These scenarios are given by means of a priori given compact sets, that depend on the prehistory of prices: the increments of the price at each moment of time must lie in the corresponding compact sets. The presentation focuses on achieving clarity, without aiming the greatest possible generality; this is the reason for the nature of a number of assumptions. The absence of transaction costs is assumed, and the market is considered both with and without trade constraints. The game-theoretic approach immediately allows us to write down the corresponding Bellman–Isaacs equations using economic interpretation of the problem.

中文翻译：

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确保对冲的确定性方法：金融市场模型，交易约束和Bellman-Isaacs方程

摘要

在参考时间的基础上，提出了一种保证离散时间超级复制的确定性问题设置，作为传统概率方法的一种替代方案。在提议的框架内，不需要参考措施，对冲或有债权的目的是要保证在所有可容许的情况下，在期权合同下可能的收益得到覆盖。这些情况是通过先验给定的紧缩集来给出的，这些先验紧缩集取决于价格的历史记录：每个时间的价格增量必须位于相应的紧缩集中。该演示文稿着重于实现清晰度，而没有最大可能的通用性；这就是许多假设性质的原因。假定没有交易成本，市场被视为有贸易约束和无贸易约束。博弈论方法使我们能够立即使用问题的经济解释来写下相应的Bellman-Isaacs方程。